How to prove this (Circle Problem)?

I took geometry a couple of years ago. Here is my thinking if you draw a tangent at the point where the line intersects the circle, then the tangent is parallel to the chord because it is also perpendicular to the line. (A tangent to a circle forms a right angle with the circle's radius, at the point of contact of the tangent). Therefore, since the tangent is parallel to the chord and a tangent forms a right angle to the circle's radius, the line must go through the center of the circle.